Find the measure of each marked angle. In Exercises 19–22, m a...

Question

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

Accepted Answer

Welcome back. Everyone in this problem, we want to find a measure of the indicated angles, X degrees X plus 50 degrees and 250 minus five X degrees in our triangle A says they are 50 degrees, 55 degrees and 95 degrees respectively. B says they are 2070 90 degrees C, 30 60 90 degrees and D, 40 50 90 degrees respectively. Now, how are we going to figure out the measure of our indicated angles? Well, let's call our angles A B and the sea. What do we know about angles in a triangle? We'll recall that the sum of angles in a triangle equal 180. OK. Sum of angles in a triangle. It is 180 degrees. So that means then that for this triangle, A plus B plus C equals 180 degrees. If we can substitute our expressions in terms of X for A B and C, we should be able to sulfur X and use that value of X to sulfur our angles A B and C. So let's go ahead and do that. Now, we know that A is XB is X plus 50 degrees and C is 250 minus five X degrees. OK? So all of that is equal to 180 degrees. Now X plus X minus five X equals negative three X 50 plus 250 equals 300. OK? So negative three X plus 300 is gonna be equal to 180 degrees. And if we subtract 300 from both sides, that means negative three X equals negative 120 which means then that X equals negative 120 divided by negative three, which equals positive 40. Thus X is 40 degrees. Since we have a value of X, this tells us then that A which is X is equal to 40 degrees B which is X plus 50 is going to be 40 degrees plus 50 degrees which is 90 degrees. OK? And C which is 250 minus five, X is going to be equal to 250 minus five, multiplied by 45 multiplied by 40 is 202 150 minus 200 equals 50 degrees. Therefore, the indicated angles in our triangle are 40 degrees, 50 degrees and 90 degrees. D is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .
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Key Concepts

Parallel Lines and Transversals

Angle Relationships

Angle Measurement

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